Related papers: A note on restricted X-ray transforms

In this paper, we present a novel approach to the problem of merging of B\'ezier curves with respect to the $L_2$-norm. We give illustrative examples to show that the solution of the conventional merging problem may not be suitable for…

We prove $L^p$ bounds in the range $1<p<\infty$ for a maximal dyadic sum operator on $\rn$. This maximal operator provides a discrete multidimensional model of Carleson's operator. Its boundedness is obtained by a simple twist of the proof…

We prove uniform $L^p \to L^q$ bounds for Fourier restriction to polynomial curves in $\mathbb R^d$ with affine arclength measure, in the conjectured range.

Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…

In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be…

A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $L^p-L^q$ restriction…

We prove certain $L^p$ estimates ($1<p<\infty$) for non-isotropic singular integrals along surfaces of revolution. As an application we obtain $L^p$ boundedness of the singular integrals under a sharp size condition on their kernels.

In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of the bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$…

Let p and q be conjugate exponents, with p in [1,2]. It is shown that the Laplace transform acts boundedly between the Lp space with unit weight on the positive real semiaxis and the Lq space weighted by a well-projected measure (a term…

We prove the $L^p (p > 3/2)$ boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.

The twisted paraproduct can be viewed as a two-dimensional trilinear form which appeared in the work by Demeter and Thiele on the two-dimensional bilinear Hilbert transform. $L^p$ boundedness of the twisted paraproduct is due to Kova\v{c},…

We establish $L^p$ error estimates for monotone numerical schemes approximating Hamilton-Jacobi equations on the $d$-dimensional torus. Using the adjoint method, we first prove a $L^1$ error bound of order one for finite-difference and…

In this paper, for general curves $(t,\gamma(t))$ satisfying some suitable curvature conditions, we obtain some $L^p(\mathbb{R})\times L^q(\mathbb{R}) \rightarrow L^r(\mathbb{R})$ estimates for the bilinear fractional integrals…

In this paper we present a generalization in the context of multilinear Muckenhoupt classes of the endpoint extrapolation theorem on restricted weights due to Carro, Grafakos and Soria. Moreover, our main result is obtained on limited…

We define variable parameter analogues of the affine arclength measure on curves and prove near-optimal $L^p$-improving estimates for associated multilinear generalized Radon transforms. Some of our results are new even in the convolution…

We prove $L^p(w)$ bounds for the Carleson operator ${\mathcal C}$, its lacunary version $\mathcal C_{lac}$, and its analogue for the Walsh series $\W$ in terms of the $A_q$ constants $[w]_{A_q}$ for $1\le q\le p$. In particular, we show…

We prove an endpoint version of the Stein-Tomas restriction theorem, for a general class of measures, and with a strengthened Lorentz space estimate. A similar improvement is obtained for Stein's estimate on oscillatory integrals of…

In this paper we address the following question: given a holomorphic function with prescribed $L^p(\mathbb{R})$ and $L^q(\mathbb{R})$ norm (with $1\leq p,q \leq \infty$) along two parallel lines in the complex plane, then what is the…

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…

We study the $L^p-L^q$ boundedness of Bergman projector on the minimal ball. This improves an important result of \cite{MY} due to G. Mengotti and E. H. Youssfi.